SOLUTION: A play was attended by 456 people. Patron's tickets cost $2 and all other tickets cost $3. If the total box office receipts were $1131, how many of each ticket was sold?

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Question 1169003: A play was attended by 456 people. Patron's tickets cost $2 and all other tickets cost $3. If the total box office receipts were $1131, how many of each ticket was sold?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
A play was attended by 456 people. Patron's tickets cost $2 and all other tickets cost $3.
If the total box office receipts were $1131, how many of each ticket was sold?
~~~~~~~~~~~~~~~~~ 


Let x = the number of the "all other tickets" at $3 each.

Then the number of the patron's tickets is  (456-x).


Now you write the total money equation (the revenue)


    3x + 2*(456-x) = 1131.


From the equation, you get


    x =  = 219.


ANSWER.  219 tickets at $3 and the rest, (456-219) = 237 tickets at $2.

Solved.

---------------

It is a standard and typical tickets problem.

There are different methods of solving such problems.
In this site, there are lessons
    - Using systems of equations to solve problems on tickets
    - Three methods for solving standard (typical) problems on tickets
explaining and showing all basic methods of solving such problems.

From these lessons,  learn on how to solve such problems once and for all.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


You can solve this kind of problem quickly using logical reasoning and simple mental arithmetic, if a formal algebraic solution is not required.

(1) If all 456 tickets were for patrons, the total cost would be $912, which is $219 less than the actual total.
(2) Since each other ticket costs $1 more than a patron's ticket, the number of other tickets was 219.
(3) And that means the number of patron's tickets sold was 456-219 = 237.

ANSWERS: 237 Patron's tickets; 219 others
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